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The Generalized Fourier Series Method - Bending of Elastic Plates (Hardcover, 1st ed. 2020)
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The Generalized Fourier Series Method - Bending of Elastic Plates (Hardcover, 1st ed. 2020)
Series: Developments in Mathematics, 65
Expected to ship within 10 - 15 working days
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This book explains in detail the generalized Fourier series
technique for the approximate solution of a mathematical model
governed by a linear elliptic partial differential equation or
system with constant coefficients. The power, sophistication, and
adaptability of the method are illustrated in application to the
theory of plates with transverse shear deformation, chosen because
of its complexity and special features. In a clear and accessible
style, the authors show how the building blocks of the method are
developed, and comment on the advantages of this procedure over
other numerical approaches. An extensive discussion of the
computational algorithms is presented, which encompasses their
structure, operation, and accuracy in relation to several
appropriately selected examples of classical boundary value
problems in both finite and infinite domains. The systematic
description of the technique, complemented by explanations of the
use of the underlying software, will help the readers create their
own codes to find approximate solutions to other similar models.
The work is aimed at a diverse readership, including advanced
undergraduates, graduate students, general scientific researchers,
and engineers. The book strikes a good balance between the
theoretical results and the use of appropriate numerical
applications. The first chapter gives a detailed presentation of
the differential equations of the mathematical model, and of the
associated boundary value problems with Dirichlet, Neumann, and
Robin conditions. The second chapter presents the fundamentals of
generalized Fourier series, and some appropriate techniques for
orthonormalizing a complete set of functions in a Hilbert space.
Each of the remaining six chapters deals with one of the
combinations of domain-type (interior or exterior) and nature of
the prescribed conditions on the boundary. The appendices are
designed to give insight into some of the computational issues that
arise from the use of the numerical methods described in the book.
Readers may also want to reference the authors' other books
Mathematical Methods for Elastic Plates, ISBN: 978-1-4471-6433-3
and Boundary Integral Equation Methods and Numerical Solutions:
Thin Plates on an Elastic Foundation, ISBN: 978-3-319-26307-6.
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